A Mean Field Game of Optimal Portfolio Liquidation

Author:

Fu Guanxing1ORCID,Graewe Paulwin2,Horst Ulrich3ORCID,Popier Alexandre4ORCID

Affiliation:

1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

2. Deloitte Consulting GmbH, 10719 Berlin, Germany

3. Department of Mathematics and School of Business and Economics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany

4. Laboratoire Manceau de Mathématiques, Le Mans Université, 72058 Le Mans Cedex 9, France

Abstract

We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with a finite terminal value yet a singular driver. Extending the method of continuation to linear-quadratic FBSDEs with a singular driver, we prove that the MFG has a unique solution. Our existence and uniqueness result allows proving that the MFG with a possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Computer Science Applications,General Mathematics

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